Flexible holder to fill cardboard tubes of different paper towels (e.g. kitchen towel)

I don't like to do anything in plastic. My favorite material is wood but 3d printing is the perfect add-on to that. So I designed one holder for workshop towels and kitchen paper towels (core ~40mm) for wood (if you are interested in the design file, done in fusion, write me). Both types have a different diameter and length.
During the years I've learned that the cardboard tubes haven't always the same diameter. For the towel rolls I'll need a flexible holder to fill the cardboard tube and fit to my 16mm wooden rod. This is the model for the holder. For best fit you need springs with an outer diameter of ~7mm and <5mm compressed. My springs have an expanded length of 20mm. The springs must not be very hard. (You can use it without springs, because this part center only)
The pin fit with it's thicker part perfect into the hole, no glue needed.